On the solutions to the normal form of the Navier-Stokes equations Ciprian FoiasLuan HoangE. OlsonMohammed Ziane 35Q3076D0537G70K45Navier-Stokes equationsfluid mechanicsnon-linear dynamicsnormal forms We introduce a construction of regular solutions to the Navier-Stokes equations that is specifically designed for the study of their asymptotic expansions. Using this construction, we give sufficient conditions for the convergence of those expansions. We also construct suitable normed spaces in which they converge. Moreover, in these spaces, the normal form of the Navier-Stokes equations associated with the terms of the asymptotic expansions (C. Foias and J.C. Saut, \textit{Asymptotic integration of Navier--Stokes equations with potential forces. I}, Indiana Univ. Math. J. \textbf{40} (1991), 305-320) is a well-behaved infinite system of differential equations. Indiana University Mathematics Journal 2006 text pdf 10.1512/iumj.2006.55.2830 10.1512/iumj.2006.55.2830 en Indiana Univ. Math. J. 55 (2006) 631 - 686 state-of-the-art mathematics http://iumj.org/access/